With the improvement in the level of science and technology and the improvement of people’s living standards, the functions of traditional manual wheelchairs have been unable to meet people’s living needs. Therefore, traditional wheelchairs have been gradually replaced by smart wheelchairs. Compared with traditional wheelchairs, smart wheelchairs have the characteristics of light operation and faster speed. However, when driving on some complex road surfaces, the vibration generated by the bumps of the motorcycle will cause damage to the human body, so wheelchairs with good electric power and stability can better meet the needs of people and make up for their travel needs. Based on the traditional vehicle stability analysis method, the mathematical theory of roll stability and pitch stability of the wheelchair–human system was established. We built a multi-body dynamics model with human skeleton and joint stiffness based on the multi-body dynamics method. The functioning of the wheelchair–human system was simulated and analyzed on the ditch, step, and combined road. The acceleration and Euler angle changes of the human head, chest, and wheelchair truss position were obtained, and the data results were analyzed to evaluate the stability and comfort of the system. Finally, a wheelchair test platform was built, and the road driving test was carried out according to the simulation conditions to obtain the system acceleration and angle data during the driving process. The simulation analysis was compared to verify the accuracy of the multi-body dynamics method, and the stability and comfort of the system were evaluated.